A distributed UAV SAR tomographic three-dimensional imaging method based on time-division stepped frequency waveform

Abstract

The present invention relates to a distributed unmanned aerial vehicle SAR tomography three-dimensional imaging method based on a time-division stepped frequency waveform, which belongs to the technical fields of urban surveying and mapping, station field investigation, disaster relief, etc., and can realize the signal acquisition of a single and double base station hybrid configuration of a distributed unmanned aerial vehicle SAR system, and can obtain a two-dimensional image for an N-station system to realize elevation sampling and three-dimensional imaging. In the method of the present invention, the distributed unmanned aerial vehicle adopts a time-division stepped frequency waveform when performing polling transmission to realize polling between each unmanned aerial vehicle, so as to ensure that the SAR on any unmanned aerial vehicle can receive the direct wave and backscattered echo from the SAR on other unmanned aerial vehicles and the backscattered echo of the SAR on the unmanned aerial vehicle.

Description

Technical Field

[0001] The present invention relates to a distributed UAV SAR tomographic three-dimensional imaging method based on time-division stepped frequency waveform, which belongs to the technical fields of urban surveying and mapping, station field reconnaissance, disaster rescue, etc., and can realize the signal acquisition of a single-double base station hybrid configuration of a distributed UAV SAR system. For an N-station system, the signal acquisition can be obtained. A two-dimensional image is used to achieve elevation sampling and three-dimensional imaging. Background Art

[0002] TomoSAR obtains the resolution of the third dimension by synthesizing an aperture in the height dimension. It avoids the problems of overlap and top-bottom inversion by restoring the real three-dimensional (3D) spatial information of the target, thus outperforming traditional two-dimensional (2D) SAR imaging. Multi-baseline tomographic SAR is an extension of traditional two-dimensional SAR. It refers to combining a certain number of two-dimensional SAR images obtained on radar motion trajectories that meet a certain distribution law, constructing a spatial baseline in the normal direction of the two-dimensional SAR imaging plane (hereinafter referred to as the height direction), and then using the aperture synthesis theory to establish an equivalent aperture to obtain high resolution in the height direction. Unmanned aerial vehicles (UAVs) are an important development direction for airborne TomoSAR in the future, especially small UAVs, which are fast to deploy and flexible to fly. They have broad application prospects in urban three-dimensional reconstruction, urban management, and emergency detection.

[0003] Frequency stepped waveform (SFW) is a waveform widely used in high-resolution radar in recent years. It transmits a set of pulse signals with different carrier frequencies, where the carrier frequency of the signal can be linear step, nonlinear step or random frequency, and obtains high-resolution range image through range image synthesis method or bandwidth synthesis method. Since the bandwidth of each pulse is much smaller than the total bandwidth of the synthesis, the instantaneous bandwidth of the system receiver only needs to meet the bandwidth of the pulse rather than the total bandwidth of the synthesis, which greatly reduces the instantaneous bandwidth of the system. Compared with other signal systems, frequency stepped signals have the advantages of flexible waveform design, small instantaneous bandwidth, low hardware requirements and low cost. Therefore, frequency stepped waveforms are often used in unmanned aerial vehicle SAR.

[0004] However, existing multi-baseline tomographic SAR mostly adopts a single-machine multi-pass method, which has slow response and long time consumption, and is inconvenient to apply in various fields. Distributed UAV SAR is a SAR system mounted on a distributed UAV platform, which can obtain multi-baseline data in one pass and has the advantage of fast response. For distributed UAV SAR systems, the use of traditional frequency stepped waveforms cannot meet the needs of multiple UAVs to transmit and receive echo signals at the same time, and cannot realize single and double base station configuration signal acquisition. Summary of the invention

[0005] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art and propose a distributed UAV SAR tomographic three-dimensional imaging method based on a time-division stepped frequency waveform, which solves the problem of data acquisition of the distributed UAV SAR system, realizes the signal acquisition of a single and double base station hybrid configuration, obtains multiple two-dimensional images to construct an elevation baseline and realizes three-dimensional inversion.

[0006] The technical solution of the present invention is:

[0007] A distributed UAV SAR tomographic three-dimensional imaging method based on time-division stepped frequency waveform, the method comprising the following steps:

[0008] In the first step, the distributed UAV performs polling transmission and receives each sub-band signal of the stepped frequency. The distributed UAV adopts a time-division stepped frequency waveform when performing polling transmission. When receiving the echo signal of each sub-band signal of the stepped frequency, the echo signal is first demodulated, and then the amplitude and phase error compensation is performed;

[0009] In the second step, the step frequency sub-band signals in the first step are pre-distorted, and the sub-band splicing and inter-sub-band error compensation are performed on the pre-distorted step frequency sub-band signals to improve the range resolution and obtain echo data;

[0010] The third step is to obtain a SAR image using a three-dimensional BP tomography SAR imaging algorithm based on the echo data obtained in the second step.

[0011] In the first step, the distributed UAV refers to a UAV with a distributed structure. The distributed structure means splitting the current integrated functional system into several physically separated, relatively simple, and relatively specialized subsystems, and maintaining or expanding the original functions through information exchange. ;

[0012] In the first step, each sub-band signal of the stepped frequency is a group of narrow-band signals whose center frequency steps by Δf, and the frequency modulation slope of each narrow-band signal is K r , the narrowband signal pulse repetition period is PRT;

[0013] The echo signal of the nth sub-band signal in each sub-band signal of the stepped frequency is described by the following formula:

[0014]

[0015] Where σ is the target backscatter coefficient, rect[.] is the rectangular window function, t is the distance time, c is the speed of light, and f c (n) is the center frequency of the nth sub-band signal, R is the target distance, T p is the pulse width;

[0016] In the second step, the method of inter-subband error compensation is: a method of fitting the trend of the phase distortion value using a support vector regression algorithm, wherein a radial basis function is used as a kernel function, and a γ value of the radial basis function is determined using F1;

[0017] In the first step, when polling transmission is performed, the SAR on each UAV works simultaneously and takes turns at a time interval t. u Transmit each sub-band signal of the stepped frequency in time, and PRT=n*t u , which contains 1*t u The emission period and (n-1)*t u The receiving cycle;

[0018] In the third step, the three-dimensional BP tomography SAR imaging algorithm refers to: taking the echo data obtained in the second step as input, calculating the echo delay after range pulse compression processing, then performing range interpolation and resampling, compensating for the residual phase, and finally performing coherent accumulation of the processed signal to complete SAR imaging.

[0019] Beneficial Effects

[0020] (1) In the method of the present invention, the distributed UAVs use a time-division stepped frequency waveform to perform polling transmission and receive stepped frequency sub-band signals, so that the SAR on any UAV can receive the direct wave and backscattered echo from the SAR on other UAVs and the backscattered echo of the SAR on the UAV;

[0021] (2) In the method of the present invention, a set of narrowband signals with a center frequency stepped by Δf is used as the transmission signal when the UAV SAR performs polling, and the distributed frequency stepped SAR system waveform is used to realize hybrid configuration data acquisition, thereby reducing the impact of time synchronization error on coherence performance, thereby reducing the demand for time synchronization accuracy;

[0022] (3) In the method of the present invention, the echo signal of the sub-band signal is demodulated and the amplitude and phase errors are compensated to eliminate the influence of the distance on the broadband splicing process;

[0023] (4) In the method of the present invention, a method of fitting the trend of phase distortion value by support vector regression algorithm is adopted during inter-subband error compensation to compensate for the high-frequency phase fluctuation at zero frequency caused by orthogonal modulation;

[0024] (5) In the method of the present invention, when performing polling transmission, the SAR on each UAV works simultaneously and takes turns to transmit at a time interval t u Transmit stepped frequency sub-band signals in time-sharing mode to obtain high resolution in range direction;

[0025] (6) In the method of the present invention, the three-dimensional BP tomographic SAR imaging algorithm directly regards the echo data acquired by multiple flights as the echo data of the array SAR;

[0026] (7) The method of the present invention solves the problem of data acquisition of distributed UAV SAR system, realizes signal acquisition of single and double base stations in a hybrid configuration, has higher performance, obtains multiple two-dimensional images to construct elevation baselines and realizes three-dimensional inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A time-frequency correspondence diagram of a frequency-stepped SAR transmission signal in an embodiment of the present invention;

[0028] Figure 2 It is a waveform diagram applied to TomoSAR in an embodiment of the present invention. DETAILED DESCRIPTION

[0029] The present invention will be further described below in conjunction with the accompanying drawings.

[0030] The three-dimensional imaging method of the present invention comprises the following steps:

[0031] Step 1: The distributed UAV performs polling transmission and receives each sub-band signal of the stepped frequency. The distributed UAV adopts a time-division stepped frequency waveform when performing polling transmission. When receiving the echo signal of each sub-band signal of the stepped frequency, the echo signal is first demodulated, and then the amplitude and phase error compensation is performed.

[0032] By transmitting a group of narrowband signals with different center frequencies, high resolution in the range direction can be obtained. Figure 1 is the time-frequency relationship diagram of the transmitted signal, where T p is the pulse width of the narrowband signal, B is the bandwidth of the narrowband signal, Δf is the step interval between adjacent narrowband signals, PRT is the narrowband signal pulse repetition period, f c (n) is the center carrier frequency of the nth narrowband signal, n is the number of narrowband signals in a pulse group, f c (1) is the center carrier frequency of the first narrowband signal, f c (2) is the center carrier frequency of the second narrowband signal, f c (3) is the center carrier frequency of the third narrowband signal;

[0033] Assume that the frequency modulation slope of the transmitted signal is K r , and the distance between a certain point P and the radar is R, then the nth generation narrowband echo signal received by the radar is

[0034]

[0035] Among them, σ is the target backscatter coefficient, rect[.] is the rectangular window function, t is the distance time, and c is the speed of light. c (n) can be expressed as

[0036] f c (n) = f c +nf n=0,1,...,N (2)

[0037] Among them, f c is the center frequency of the first narrowband signal.

[0038] After demodulation, the nth generation narrowband echo signal is expressed as

[0039]

[0040] Among them, f r is the distance frequency.

[0041] The above analysis is a study of the transmission echo signal under the ideal state of the system. However, in general, the non-ideal factors of the system components will introduce unavoidable amplitude and phase errors in the echo signal and affect the range-direction broadband splicing process. Therefore, it is necessary to consider the amplitude and phase errors in the echo signal.

[0042] Assume that the frequency domain amplitude and phase errors contained in the nth narrowband signal received by the radar are A and n (f r ) and θ n (f r ), then the demodulated nth generation narrowband echo signal is expressed as

[0043]

[0044] Since each narrowband signal passes through the same system loop during transmission and reception, it can be considered that the amplitude and phase errors contained in each narrowband signal are small and negligible, that is, A n (f r ) and θ n (f r ) does not change with the frequency n.

[0045] To ensure that any station can receive direct waves and backscattered echoes from all other stations in all dual-base configurations and backscattered echoes in all monostatic configurations. A time-division waveform is designed. The waveform mechanism is as follows: when a certain drone transmits a signal, other drones can only receive the signal. In a full round, all drones transmit signals one by one, and then a new round of transmission begins. The TomoSAR prototype consists of four drones, and the time between two adjacent transmissions is t uTherefore, the actual PRT of each drone is 4t u The time-division waveform used is as follows: Figure 2 shown.

[0046] Take drone 1 transmitting and another receiving as an example to explain the specific parameter configuration. The pulse width of the transmitted signal is 2.5μs. The interval between the end of drone 1's transmission and the beginning of the receiving window is 1.5μs, and the total receiving window length is 8μs. To avoid direct wave loss caused by time synchronization error, the receiving windows of drones 2, 3, and 4 are opened 400ns ahead of the start of drone 1's transmission pulse, as shown in Figure 1. Figure 2 The receiving window lengths of drones 2, 3, and 4 are all 12 μs, of which the direct wave receiving time is 4 μs and the backscattered echo receiving time is 8 μs. Figure 2 As shown in the last row. The launch of drones 2, 3, and 4 is similar and will not be repeated. The time between two adjacent launches is 400μs, so the final PRT used for imaging is 1600μs. Such parameter configuration can achieve an observable range of 600-1900m.

[0047] Step 2: pre-distortion processing is performed on each sub-band signal of the stepped frequency in the first step, and sub-band splicing and inter-sub-band error compensation are performed on each sub-band signal of the stepped frequency after the pre-distortion processing, so as to improve the range resolution and obtain echo data;

[0048] In order to compensate for the high-frequency phase fluctuation at zero frequency caused by orthogonal modulation, the support vector regression algorithm (SVR) is used to fit the trend of the phase distortion value to obtain the global optimal solution. The radial basis function (RBF) is used as the kernel function, and the F1 score in statistics is used to determine the γ value in the RBF. All frame phase distortion values ​​are used as samples, and 70% of them are randomly selected as the training set, and the rest are cross-validation sets; according to the fitting accuracy of the fitted curve in the two sets, the accuracy rate r is determined. prec and recall r rec , the F1 score is defined as the harmonic mean of the two:

[0049]

[0050] The γ value that makes the F1 score the highest is obtained through fitting, and the best phase distortion fitting value is obtained. According to this method, the amplitude distortion value is fitted.

[0051] Next, the amplitude and phase errors in the sub-band extracted from the calibration signal are compensated to the frequency domain of the echo data, and each sub-band is imaged separately to obtain the image of each sub-band channel. The point target signal model of the nth sub-band after imaging is expressed as:

[0052]

[0053] The last term is due to the fact that the subband signals are collected at different pulse repetition intervals. To compensate for this term, we use the azimuth time shift method. The specific method is to first n ing The (t,η) signal is transformed to the range Doppler domain and then multiplied by the following formula:

[0054]

[0055] Next, contrast is used to evaluate the multivariable optimization problem of multi-subband channel error estimation. Image contrast can be obtained by the following formula:

[0056]

[0057] Its cost function can be written as:

[0058]

[0059] where ω n Is a complex number, representing the compensated amplitude and phase error between the nth sub-band and the reference sub-band. n ing (t,η) represents the compensation C n as (f η ) after distance upsampling. In order to perform sub-band splicing, each sub-band image needs to be frequency-shifted to the corresponding frequency range according to the step frequency relationship, and then multiplied by H after distance upsampling. n rf (t):

[0060]

[0061] In the multi-subband system experiment, a subband is first selected as a reference channel, and a genetic algorithm is used to find the solution to the optimization problem. In the process, a group of solutions is randomly generated to form a population; in each subsequent optimization step, the cost function of the entire population is calculated to obtain an ordered list of solutions. After 5 iterations, the optimal solution has been basically found.

[0062] Step 3: Based on the echo data obtained in the second step, a SAR image is obtained using a three-dimensional BP tomography SAR imaging algorithm.

[0063] The multi-baseline tomographic SAR imaging algorithm based on three-dimensional BP directly treats the echo data obtained from multiple flights as the echo data of array SAR. At each azimuth slow moment, the antennas of multiple platforms receive the echo signal. After the echo data obtained by each flight platform are compressed, the echo delay from each grid point in the three-dimensional imaging space to each flight platform at each azimuth slow moment is calculated, and the residual phase is compensated in the data domain. Finally, the data of each azimuth slow moment of each flight platform are accumulated together to obtain the backscattering coefficient distribution of each grid point in the three-dimensional imaging space.

[0064] The multi-baseline tomographic SAR imaging method based on the three-dimensional BP algorithm has the following specific processing steps:

[0065] (1) Range pulse compression of echo data: Use matched filtering technology to perform range compression on the echo data obtained from each flying platform. The reference function of range matched filtering is:

[0066] H r (t) = exp{-jπK r t 2}t∈[-T r / 2,T r / 2,] (11)

[0067] Among them, K r =B / T r represents the signal modulation frequency, B represents the transmission signal bandwidth, T r Indicates the pulse width of the transmitted signal in the time domain. Generally, pulse compression is implemented in the frequency domain, the signal and the reference function are transformed into the frequency domain, and then the pulse compressed data is transformed back to the time domain through Fourier transform. Assume that the echo signal after range compression is denoted as g n .

[0068] (2) Calculate the slant distance from each imaging grid to the radar platform in the imaging scene and calculate the echo delay; then divide the grid on the azimuth-altitude plane, and each grid represents an azimuth slow moment and an altitude position. Then, calculate the delay of the echo between the phase center of the nth transmitting antenna at the jth azimuth slow moment and the grid point i, that is, calculate the distance between the two The delay calculation expression is:

[0069]

[0070] (3) Distance interpolation and resampling: The sinc function is used as the interpolation kernel to interpolate the discrete data after distance compression, and the grid point τ is obtained through sampling. nij Data I i (n).

[0071] (4) Compensate for the residual phase. The echo data of the grid point obtained by interpolation is in the form of a complex number. To achieve coherent superposition of all data within the grid point, it is necessary to compensate for the phase information of the complex number. The two-way distance from the grid point i to each passing platform at the jth azimuth slow time obtained according to (2) is Compensate the residual phase. The residual phase compensation factor is expressed as:

[0072]

[0073] Among them, f c Indicates carrier frequency

[0074] The data I obtained by interpolation and resampling (3) i (n) and the phase compensation factor H c By multiplying (j,n), we can obtain the back projection signal related to the flying platform n:

[0075]

[0076] Among them, r i is the position vector of grid point i, a k and b k They represent the starting and ending positions of the synthetic aperture in azimuth at grid point i, represents the position vector of the radar platform, is the distance between grid point i and each flying platform n, g n (.) represents the echo data after distance compression of the nth flight track, k c =2πf c / c is the wave number.

[0077] (5): Perform coherent accumulation on the signal, add up the amplitudes of these echo data, and obtain the back projection information v of the grid point i in the tomographic direction, that is:

[0078]

[0079] For each grid, repeat the process from (3) to (5) to obtain the backscatter coefficient distribution of all grid points in the three-dimensional imaging space and complete the reconstruction of the scene. According to the steps of the tomographic SAR imaging method of the three-dimensional BP algorithm, this method only uses the three-dimensional geometric position relationship between the imaging grid and the radar platform trajectory, and has nothing to do with whether the track platform is non-uniformly distributed.

Claims

1. A distributed UAV SAR tomographic three-dimensional imaging method based on time-division stepped frequency waveform, characterized in that The steps of the method include: In the first step, the distributed UAV performs polling transmission and receives each sub-band signal of the stepped frequency. The distributed UAV adopts a time-division stepped frequency waveform when performing polling transmission. When receiving the echo signal of each sub-band signal of the stepped frequency, the echo signal is first demodulated, and then the amplitude and phase error compensation is performed; The second step is to perform pre-distortion processing on the sub-band signals of the stepped frequencies in the first step, and perform sub-band splicing and inter-sub-band error compensation on the sub-band signals of the stepped frequencies after the pre-distortion processing to obtain echo data; The third step is to obtain a SAR image using a three-dimensional BP tomography SAR imaging algorithm based on the echo data obtained in the second step; In the first step, each sub-band signal of the stepped frequency is a group of narrow-band signals whose center frequency steps by Δf, and the frequency modulation slope of each narrow-band signal is K r , the narrowband signal pulse repetition period is PRT; the echo signal of the nth sub-band signal in each sub-band signal of the stepped frequency is shown as follows: Where σ is the target backscatter coefficient, rect[.] is the rectangular window function, t is the distance time, c is the speed of light, and f c (n) is the center frequency of the nth sub-band signal, R is the target distance, T p is the pulse width. If there are N sub-band signals, the center frequency of the nth sub-band signal is f c (n) = f c +nΔf n=0,1,…,N; In the third step, the three-dimensional BP tomography SAR imaging algorithm refers to: using the echo data obtained in the second step as input, performing range pulse compression processing, then calculating the echo delay, then performing range interpolation, compensating the residual phase in the data domain, and finally performing coherent accumulation of the signal to complete SAR imaging; The method for performing range pulse compression processing on the echo data is to use a matched filtering method to perform range compression on the echo data obtained by each flying UAV SAR. The reference function of the range matched filtering is: H r (t)=exp{-jπK r t 2 }t∈[-T r / 2,T r / 2,] Among them, K r =B / T r represents the signal modulation frequency, B represents the transmission signal bandwidth, T r represents the pulse width of the transmitted signal in the time domain, realizes pulse compression in the frequency domain, transforms the signal and the reference function into the frequency domain, and then transforms the pulse compressed data back to the time domain through Fourier transform. Let the echo signal after range compression be denoted as g n ; The method for calculating the echo delay is as follows: calculating the slant distance from each imaging grid in the imaging scene to the radar platform, and then dividing the grid on the azimuth-altitude plane, each grid represents an azimuth slow moment and an altitude position, and calculating the delay of the echo between the phase center of the nth transmitting antenna at the jth azimuth slow moment and the grid point i, that is, calculating the distance between the two The expression of echo delay is: The distance interpolation method is as follows: using the sinc function as the interpolation kernel, interpolating the discrete data after distance compression, and obtaining a time domain signal after distance interpolation; The method for compensating the residual phase in the data domain is: obtaining the grid point τ by sampling nij Data I i (n), the two-way distance from grid point i to each passing UAV SAR at the jth azimuth slow time Compensate the residual phase, the residual phase compensation factor is expressed as: Among them, f c Indicates the carrier frequency, the data I i (n) and the phase compensation factor H c (j,n) to obtain the back-projected signal related to the flying UAV SARn: Among them, r i is the position vector of grid point i, a k and b k They represent the starting and ending positions of the synthetic aperture in azimuth at grid point i, represents the position vector of the radar platform, is the distance between grid point i and each passing UAV SARn, g n (.) represents the echo data after distance compression of the nth flight track, k c =2πf c / c is the wave number; The method for coherently accumulating the signal is: adding the amplitudes of the echo data to obtain the back projection information v of the grid point i in the tomographic direction, that is:

2. The distributed UAV SAR tomographic three-dimensional imaging method based on time-division stepped frequency waveform according to claim 1 is characterized in that: In the first step, the echo signal of the nth sub-band signal is demodulated to obtain the nth sub-generation narrow-band echo signal as shown in the following formula: Among them, f r is the distance frequency.

3. The distributed UAV SAR tomographic 3D imaging method based on time-division stepped frequency waveform according to claim 2, characterized in that: The method for compensating the amplitude and phase errors of the obtained n-th generation narrowband echo signal is as follows: Assume that the frequency domain amplitude and phase errors contained in the nth narrowband signal received by the SAR on the drone are A and n (f r ) and θ n (f r ), the compensated n-th generation narrowband echo signal is expressed as:

4. The distributed UAV SAR tomographic 3D imaging method based on time-division stepped frequency waveform according to claim 3 is characterized in that: In the second step, the support vector regression algorithm is used to fit the trend of the phase distortion value during the inter-subband error compensation, the radial basis function is used as the kernel function, and the γ value of the radial basis function is determined by using F1, specifically: All frame phase distortion values ​​are taken as samples, 60%-70% of them are randomly selected as training sets, and the rest are cross-validation sets. The accuracy rate r is determined based on the fitting accuracy of the fitted curve in the two sets. prec and recall r rec , the F1 score is defined as the harmonic mean of the two: After fitting, the γ value that gives the highest F1 score is obtained, the best phase distortion fitting value is obtained, and the amplitude distortion value is fitted.

5. The distributed UAV SAR tomographic 3D imaging method based on time-division stepped frequency waveform according to claim 1, characterized in that: In the first step, when polling transmission is performed, the SAR on each UAV works simultaneously and takes turns at a time interval t. u The stepped frequency sub-band signals are transmitted in time division, and the repetition period PRT = n*t u , the repetition period contains 1*t u The emission period and (n-1)*t u The receiving cycle.

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